A lot of the answers to your questions depend on where you dive and for what fish, and you don't seem to divulge that information. However, based on your user name, I'm going to assume that you are in Southern California and aspire to be able to handle a nice sized yellowtail or white sea bass.
I use Spectra on all my reels, and I think you need a minimum of 100 feet, with 150 feet being better. A big white sea bass can wind line all through the kelp and spool you even in shallow water, and you can't get directly over the fish.
Thickness- the thicker the better, but that is as long as you have a big enough reel to have at least 100 feet of it. I grip the line with my hand to create drag, and if you are trying to stop a big fish and force it to tie up in the kelp before it gets to the bottom, it will cut right through a glove if its thin.
Masahiro Mori (morifsh@aol.com), (310) 628-8082 is a dealer for Marlow Spectra and sells it much cheaper than it can be bought at West Marine. On my largest reels, I use 3 mm line (30 cents/foot) but that takes a big reel.
A nice compromise is his 2.5 mm line. Marlow doesn't usually made that thickness, but Mori got them to do a special run of it as a compromise between the 3 mm, which is too thick for a lot of reels, and 2 mm, which is harder to handle.
If you can't get enough 2.5 mm on the reel, then my favorite is the 2 mm bright yellow kite line Spectra available by scrolling to the bottom of this page.
Bulk Spectra Line at WindPower Sports Kite Store
It shows up very well down in the shade and murk, and it has a very tight weave and good stiffness so that its not limp all over you.
The stuff on the black gun with an Aimrite reel is the kite line, and the stuff on the Rob Allen stainless steel reel is the 2.5 mm.